A fractional-order difference Cournot duopoly game with long memory

We reconsider the Cournot duopoly problem in light of the theory for long memory. We introduce the Caputo fractional-order difference calculus to classical duopoly theory to propose a fractional-order discrete Cournot duopoly game model, which allows participants to make decisions while making full use of their historical information. Then we discuss Nash equilibria and local stability by using linear approximation. Finally, we detect the chaos of the model by employing a 0-1 test algorithm

Variable guiding strategies in multi-exits evacuation: Pursuing balanced pedestrian densities

Evacuation assistants and their guiding strategies play an important role in the multi-exits pedestrian evacuation. To investigate the effect of guiding strategies on evacuation efficiency, we propose a force-driven cellular automaton model with adjustable guiding attractions imposed by the evacuation assistants located in the exits. In this model, each of the evacuation assistants tries to attract the pedestrians in the evacuation space towards its own exit by sending a quantifiable guiding signal, which may be adjusted according to the values of pedestrian density near the exit. The effects of guiding strategies pursuing balanced pedestrian densities are studied. It is observed that the unbalanced pedestrian distribution is mainly yielded by a snowballing effect generated from the mutual attractions among the pedestrians, and can be suppressed by controlling the pedestrian densities around the exits. We also reveal an interesting fact that given a moderate target density value, the density control for the partial regions (near the exits) could yield a global effect for balancing the pedestrians in the rest of the regions and hence improve the evacuation efficiency. Our findings may contribute to give new insight into designing effective guiding strategies in the realistic evacuation process.Comment: 13 pages, 12 figure